/*
* INSANE - Interactive Structural Analysis Environment
*
* Copyright (C) 2003-2005
* Universidade Federal de Minas Gerais
* Escola de Engenharia
* Departamento de Engenharia de Estruturas
* 
* Author's email :    insane@dees.ufmg.br
* Author's website :  http://www.dees.ufmg.br/insane
* 
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or any later version.
* 
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
* GNU General Public License for more details.
* 
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
*/
package br.ufmg.dees.insane.shape;

import br.ufmg.dees.insane.util.IMatrix;


/**
*A class representing a shape function for the RMCIQ4 element.
*
*@author Samir
*@version 1.0
*@since 06/11/06
*/

public class RMCIQ9 extends Q9 {
	private static final long serialVersionUID = 1L;

    /* (non-Javadoc)
     * @see br.ufmg.dees.insane.shape.Shape2D#getType()
     */
    public String getType() {
        return "RMCIQ9";
    }
    
    public IMatrix getAPT(double[] g, IMatrix cN){
		IMatrix APT = new IMatrix(2,24);
		APT.setZero();
		
    	double e = g[0];
		double n = g[1];
		
//		double n00 = 0.5*e*(1+e)*0.5*n*(1+n);
//		double n10 = 0.5*e*(e-1)*0.5*n*(1+n);
//		double n20 = 0.5*e*(1+e)*(1-n*n);
//		double n30 = 0.5*e*(e-1)*(1-n*n);
//		double n40 = 0.5*e*(1+e)*0.5*n*(n-1);
//		double n50 = 0.5*e*(e-1)*0.5*n*(n-1);
//		
//		double n01 = 0.5*e*(1+e)*0.5*n*(1+n);
//		double n11 = 0.5*e*(1+e)*0.5*n*(n-1);
//		double n21 = (1-e*e)*0.5*n*(1+n);
//		double n31 = (1-e*e)*0.5*n*(n-1);
//		double n41 = 0.5*e*(e-1)*0.5*n*(1+n);
//		double n51 = 0.5*e*(e-1)*0.5*n*(n-1);
//		
//		APT.setElement(0,0,n00);
//		APT.setElement(0,2,n10);
//		APT.setElement(0,4,n20);
//		APT.setElement(0,6,n30);
//		APT.setElement(0,8,n40);
//		APT.setElement(0,10,n50);
//		
//		APT.setElement(1,13,n01);
//		APT.setElement(1,15,n11);
//		APT.setElement(1,17,n21);  
//		APT.setElement(1,19,n31);
//		APT.setElement(1,21,n41);
//		APT.setElement(1,23,n51);

		double a = Math.sqrt(3);
		
		double A1 = 1 + a*e;
		double B1 = 1 - a*e;
		double A2 = 1 + a*n;
		double B2 = 1 - a*n;
		
		double e1 = e*(1 + e);		
		double e2 = 1 - (e*e);
		double e3 = e*(e - 1);
//		double e3 = e*(1 - e);
		
		double n1 = n*(1 + n);		
		double n2 = 1 - (n*n);
		double n3 = n*(n - 1);
//		double n3 = n*(1 - n);
		
		double n00 = 0.25*A1*n1;
		double n10 = 0.25*B1*n1;
		double n20 = 0.5*A1*n2;
		double n30 = 0.5*B1*n2;
		double n40 = 0.25*A1*n3;
		double n50 = 0.25*B1*n3;
		
		double n01 = 0.25*A2*e1;
		double n11 = 0.25*B2*e1;
		double n21 = 0.5*A2*e2;
		double n31 = 0.5*B2*e2;
		double n41 = 0.25*A2*e3;
		double n51 = 0.25*B2*e3;
		
		APT.setElement(0,0,n00);
		APT.setElement(0,2,n10);
		APT.setElement(0,4,n20);
		APT.setElement(0,6,n30);
		APT.setElement(0,8,n40);
		APT.setElement(0,10,n50);
		
		APT.setElement(1,13,n01);
		APT.setElement(1,15,n11);
		APT.setElement(1,17,n21);  
		APT.setElement(1,19,n31);
		APT.setElement(1,21,n41);
		APT.setElement(1,23,n51);
		
		return APT;
    }

    public IMatrix samplingPoints(){
    	IMatrix sp = new IMatrix(12,2);
    	sp.setZero();
    	
    	double a = 1.0/Math.sqrt(3);
    	
    	sp.setElement(0,0,a);
    	sp.setElement(0,1,1);
    	sp.setElement(1,0,-a);
    	sp.setElement(1,1,1);
    	sp.setElement(2,0,a);
    	sp.setElement(3,0,-a);
    	sp.setElement(4,0,a);
    	sp.setElement(4,1,-1);
    	sp.setElement(5,0,-a);
    	sp.setElement(5,1,-1);
    	sp.setElement(6,0,1);
    	sp.setElement(6,1,a);
    	sp.setElement(7,0,1);
    	sp.setElement(7,1,-a);
    	sp.setElement(8,1,a);
    	sp.setElement(9,1,-a);
    	sp.setElement(10,0,-1);
    	sp.setElement(10,1,a);
    	sp.setElement(11,0,-1);
    	sp.setElement(11,1,-a);
    	
    	return sp;
    }

}
